First of all, we must note that not all of the people who settled the Great Plains did give up and leave. While many did leave, many also stayed.
That said, there were serious problems that faced settlers on the Great Plains. The major issue is that the plains were not really a great place for farming given the technology of the day. Farming was a very chancy thing due largely to the climate. The rains were not reliable and farmers could have their crops devastated by drought or by any number of other problems. The climate also made life in general difficult, particularly in the winters.
Largely for these reasons, the Great Plains were not a very good place for small farmers. Many of them left because of these difficulties. This area was much more conducive to the large corporate farming operations known as the “bonanza farms.”